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Linear algebra tools for data mining
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Description
Rating
Title
Linear
algebra
tools
for
data
mining
Creator
Simovici, Dan A.
Contributors
World Scientific (Firm)
DescriptionAbstract
This
comprehensive
volume
presents
the
foundations
of
linear
algebra
ideas
and
techniques
applied
to
data
mining
and
related
fields
.
Linear
algebra
has
gained
increasing
importance
in
data
mining
and
pattern
recognition
, as
shown
by the
many
current
data
mining
publications
, and has a
strong
impact
in
other
disciplines
like
psychology
,
chemistry
, and
biology
. The
basic
material
is
accompanied
by
more
than
550
exercises
and
supplements
,
many
accompanied
with
complete
solutions
and
MATLAB
applications
.
DescriptionTable Of Contents
1
.
Modules
and
linear
spaces
.
1.1
.
Introduction
.
1.2
.
Permutations
.
1.3
.
Groups
,
rings
, and
fields
.
1.4
.
Closure
and
interior
systems
.
1.5
.
Modules
.
1.6
.
Linear
mappings
.
1.7
.
Submodules
.
1.8
.
Linear
combinations
.
1.9
. The
lattice
of
submodules
of a
module
.
1.10
.
Linear
independence
.
1.11
.
Linear
spaces
.
1.12
.
Module
isomorphism
theorems
.
1.13
.
Direct
sums
and
direct
products
.
1.14
.
Dual
modules
and
linear
spaces
.
1.15
.
Topological
linear
spaces

2
.
Matrices
.
2.1
.
Introduction
.
2.2
.
Matrices
with
arbitrary
elements
.
2.3
.
Rings
and
matrices
.
2.4
.
Special
classes
of
matrices
.
2.5
.
Complex
matrices
.
2.6
.
Partitioned
matrices
and
matrix
operations
.
2.7
.
Invertible
matrices
.
2.8
.
Matrices
and
linear
transformations
.
2.9
. The
notion
of
rank
.
2.10
.
Matrix
similarity
and
congruence
.
2.11
.
Linear
systems
and
matrices
.
2.12
. The
row
echelon
form
of
matrices
.
2.13
. The
Kronecker
and
Hadamard
products
.
2.14
.
Linear
inequalities
.
2.15
.
Complex
multilinear
forms

3
.
MATLAB
.
3.1
.
Introduction
.
3.2
. The
interactive
environment
of
MATLAB
.
3.3
.
Number
representation
and
arithmetic
computations
.
3.4
.
Matrices
representation
.
3.5
.
Random
matrices
.
3.6
.
Control
structures
.
3.7
.
Indexing
.
3.8
.
Functions
.
3.9
.
Matrix
computations

4
.
Determinants
.
4.1
.
Introduction
.
4.2
.
Multilinear
forms
.
4.3
.
Cramer's
formula
.
4.4
.
Partitioned
matrices
and
determinants

5
.
Norms
on
linear
spaces
.
5.1
.
Introduction
.
5.2
.
Fundamental
inequalities
.
5.3
.
Metric
spaces
.
5.4
.
Norms
.
5.5
.
Vector
norms
on
Rn
.
5.6
. The
topology
of
normed
linear
spaces
.
5.7
.
Norms
for
matrices
.
5.8
.
Matrix
sequences
and
matrix
series
.
5.9
.
Condition
numbers
for
matrices
.
5.10
.
Conjugate
norms

6
.
Inner
product
spaces
.
6.1
.
Introduction
.
6.2
.
Inner
products
and
norms
.
6.3
.
Orthogonality
.
6.4
.
Hyperplanes
in
Rn
.
6.5
.
Unitary
and
orthogonal
matrices
.
6.6
.
Projection
on
subspaces
.
6.7
.
Positive
definite
and
positive
semidefinite
matrices
.
6.8
. The
GramSchmidt
orthogonalization
algorithm
.
6.9
. The
QR
factorization
of
matrices
.
6.10
.
Matrix
groups

7
.
Convexity
.
7.1
.
Introduction
.
7.2
.
Convex
sets
.
7.3
.
Separation
of
convex
sets
.
7.4
.
Cones
in
Rn
.
7.5
.
Convex
functions
.
7.6
.
Convexity
and
inequalities
.
7.7
.
Constrained
extrema
and
convexity

8
.
Eigenvalues
.
8.1
.
Introduction
.
8.2
.
Eigenvalues
and
Eigenvectors
.
8.3
. The
characteristic
polynomial
of a
matrix
.
8.4
.
Spectra
of
special
matrices
.
8.5
.
Geometry
of
Eigenvalues
.
8.6
.
Spectra
of
Kronecker
products
.
8.7
. The
power
method
for
Eigenvalues
.
8.8
. The
QR
iterative
algorithm

9
.
Similarity
and
spectra
.
9.1
.
Introduction
.
9.2
.
Diagonalizable
matrices
.
9.3
.
Matrix
similarity
and
spectra
.
4
. The
Sylvester
operator
.
9.5
.
Geometric
versus
algebraic
multiplicity
.
9.6
.
[symbol]matrices
.
9.7
. The
Jordan
canonical
form
.
9.8
.
Matrix
norms
and
Eigenvalues
.
9.9
.
Matrix
pencils
and
generalized
Eigenvalues
.
9.10
.
Quadratic
forms
and
quadrics
.
9.11
.
Spectra
of
positive
matrices
.
9.12
.
Spectra
of
positive
semidefinite
matrices
.
9.13
.
Kmatrices
.
MATLAB
computations

10
.
Singular
values
.
10.1
.
Introduction
.
10.2
.
Singular
values
and
singular
vectors
.
10.3
.
Numerical
rank
of
matrices
.
10.4
.
Updating
SVDs
.
10.5
.
Polar
form
of
matrices
.
10.6
.
CS
decomposition
.
10.7
.
Geometry
of
subspaces
.
10.8
.
Spectral
resolution
of a
matrix
.
MATLAB
computations
. ;
8
11
.
Graphs
and
matrices
.
11.1
.
Introduction
.
11.2
.
Graphs
.
11.3
.
Graph
connectivity
.
11.4
.
Directed
graphs
.
11.5
.
Trees
.
11.6
. The
adjacency
and
incidence
matrices
.
11.7
.
Operations
on
graphs
.
11.8
.
Digraphs
of
matrices
.
MATLAB
computations

12
.
Data
sample
matrices
.
12.1
.
Introduction
.
12.2
. The
sample
matrix
.
12.3
.
Biplots

13
.
Least
squares
approximation
and
data
mining
.
13.1
.
Introduction
.
13.2
.
Linear
regression
.
13.3
. The
least
square
approximation
and
QR
decomposition
.
13.4
.
Partial
least
square
regression
.
13.5
.
Locally
linear
embedding
.
MATLAB
computations

14
.
Dimensionality
reduction
techniques
.
14.1
.
Introduction
.
14.2
Principal
component
analysis
.
14.3
.
Linear
discriminant
analysis
.
14.4
.
Latent
semantic
indexing
.
14.5
.
Recommender
systems
and
SVD
.
14.6
.
Metric
multidimensional
scaling
.
14.7
.
Procrustes
analysis
.
14.8
.
Nonnegative
matrix
factorization

15
. The
kmeans
clustering
.
15.1
.
Introduction
.
15.2
. The
kmeans
algorithm
and
convexity
.
15.3
.
Relaxation
of the
kmeans
problem
.
15.4
.
SVD
and
clustering
.
15.5
.
Evaluation
of
clusterings
.
MATLAB
computations

16
.
Spectral
properties
of
graphs
and
spectral
clustering
.
16.1
.
Introduction
.
16.2
. The
ordinary
spectrum
of a
graph
.
16.3
. The
Laplacian
spectrum
of a
graph
.
16.4
.
Graph
cuts
,
separators
, and
clusterings
.
16.5
.
Spectral
clustering
algorithms
.
Publisher
World Scientific Pub. Co.
Subject
Parallel processing (Electronic computers).
Computer algorithms.
Identifier
9789814383509
(electronic
bk.)
;
981438349X
;
9789814383493
;
http://www.worldscientific.com/worldscibooks/10.1142/8360#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xiv, 863 p. : ill. (some col.)
Date
c2012
.
OCLC number
874497770
CONTENTdm number
423
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